Perform the multiplication a 13. (cot x+csc x)(cot x-csc x)

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Perform the multiplication a 13.  (cot x+csc x)(cot x-csc x)

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Identify Pattern: Identify the pattern in the expression. The given expression (cot x + csc x)(cot x - csc x) resembles the difference of squares pattern a^2 - b^2 = (a + b)(a - b).Apply Formula: Apply the difference of squares formula. Using the pattern a^2 - b^2 = (a + b)(a - b), we can rewrite the expression as cot^2 x - csc^2 x.Simplify Using Identities: Simplify the expression using trigonometric identities. We know that cot^2 x = (cos^2 x)/(sin^2 x) and csc^2 x = 1/(sin^2 x). Therefore, we can write cot^2 x - csc^2 x as (cos^2 x)/(sin^2 x) - 1/(sin^2 x).Combine Over Common Denominator: Combine the terms over a common denominator. Since both terms have the same denominator sin^2 x, we can combine them to get ((cos^2 x) - 1)/(sin^2 x).Use Pythagorean Identity: Use the Pythagorean identity to simplify the numerator. The Pythagorean identity states that cos^2 x + sin^2 x = 1. Therefore, cos^2 x - 1 = -(sin^2 x). We can substitute this into our expression to get -((sin^2 x)/(sin^2 x)).Final Simplification: Simplify the expression. Since sin^2 x in the numerator and denominator are the same, they cancel out, leaving us with -1.

Perform the multiplication $a^{13} (\cot x + \csc x)(\cot x - \csc x)$

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Perform the multiplication $a^{13} (\cot x + \csc x)(\cot x - \csc x)$